I understand that from mathematical point of view, only difference between Convolution and Cross Correlation is that Convolution is commutative, while Cross Correlation is not.
In many articles Cross Correlation is explained as measuring similarity between two signals, and Convolution is explained as calculating relationship between two signals.
My question is this, what is the point of commutative property? How does it make Convolution different from Cross Correlation in practice? Or is it just there for "better" mathematics and easier proofs?